The incorporation of longitudinal dynamics also allows us to identify states directly with the exact discrete symmetries, the charge conjugation \(C\)  and the mirror parity \(m_P=(-1)^JP\) . The latter is more convenient to use than parity \(P\)  in light-front dynamics [1]}. The parities associated with the quantum numbers \((n,m,l,S,J)\)  are \(m_P = (-1)^{m+S+1}\) , \(C=(-1)^{m+l+S}\) , where \(S\)  is the total spin. By contrast, LFH with IMA can only describe states with \(P = (-1)^{m+1}\)  and \(C = (-1)^{m+S}\) . In general, for states without longitudinal excitations (\(l=0\) ), e.g. \(\rho \) , \(\pi \) , \(K\) , the rest of our quantum number assignments remain the same as LFH with IMA. However, when longitudinal excitations are present in the states, e.g. \(a_0\)  (\(0^{++}\) ), \(b_1\)  (\(1^{+-}\) ), \(a_2\)  (\(2^{++}\) ), \(\rho (1700)\)  (\(1^{--}\) ), \(K_1\)  (\(1^+\) ), \(K_2\)  (\(2^-\) ), our quantum number assignments become different. It can be shown that our assignments are consistent with the discrete symmetries as well as with those of the traditional quark models [2]}.
